id large_stringlengths 9 16 | title large_stringlengths 1 382 | abstract large_stringlengths 3 6.09k | publish_date date32 | update_date date32 | categories large listlengths 1 13 | authors large_stringlengths 3 62.8k |
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alg-geom/9312006 | An algorithmic criterion for basicness in dimension 2 | We give a constructive procedure to check basicness of open (or closed)
semialgebraic sets in a compact, non singular, real algebraic surface $X$. It
is rather clear that if a semialgebraic set $S$ can be separated from each
connected component of $X\setminus(S\cup\frz S)$ (when $\frz S$ stands for the
Zariski closure ... | 1993-12-14 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | F. Acquistapace, F.Broglia, M.Pilar Velez |
alg-geom/9312008 | On the Hyperbolicity of the Complements of Curves in Algebraic Surfaces:
The Three Component Case | The paper is a contribution to the conjecture of Kobayashi that the
complement of a generic curve in the projective plane is hyperbolic, provided
the degree is at least five. Previously the authors treated the cases of two
quadrics and a line and three quadrics. The main results are Let C be the union
of three curves i... | 1993-12-14 | 2014-12-01 | [
"alg-geom",
"math.AG"
] | Gerd Dethloff, Georg Schumacher, Pit-Mann Wong |
alg-geom/9312007 | Hyperbolicity of the complement of plane algebraic curves | The paper is a contribution of the conjecture of Kobayashi that the
complement of a generic plain curve of degree at least five is hyperbolic. The
main result is that the complement of a generic configuration of three quadrics
is hyperbolic and hyperbolically embedded as well as the complement of two
quadrics and a lin... | 1993-12-14 | 2014-12-01 | [
"alg-geom",
"math.AG"
] | Gerd Dethloff, Georg Schumacher, Pit-Mann Wong |
alg-geom/9312005 | On the Hilbert Schemes of Canonically-Embedded Curves of Genus 5 and 6 | A canonically-embedded curve of genus $g$ is a pure 1-dimensional,
non-degenerate subscheme $C$ of ${\bf P}^{g-1}$ over an algebraically closed
field $k$, for which ${\cal O}_C(1) \cong \omega_C$, (the dualizing sheaf)$ and
$h^0(C, {\cal O}_C) = 1$, $h^0(C, \omega_C) = g$. The singularities of $C$ (if
any) are Gorenste... | 1993-12-10 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | John Little |
alg-geom/9312004 | On Koszul property of the homogeneous coordinate ring of a curve | The following corollary has been added: for general tetragonal curve $C$ of
genus $g\ge 9$ the homogeneous coordinate ring of $C$ defined by the line
bundle $K(-T)$, where $K$ is the canonical class, $T$ is the tetragonal series,
is Koszul. Also some misprints are corrected. | 1993-12-08 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | A. Polishchuk |
alg-geom/9312003 | Thickening Calabi-Yau moduli spaces | We describe a kind of deformation of the anti-DeRham algebra on a Calabi-Yau
manifold $X$. These are in 1-1 correspondence with the total cohomology $\oplus
H^i (X, \C)$. | 1993-12-06 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Ziv Ran |
alg-geom/9312001 | The Functor of a Smooth Toric Variety | A map Y -> P^n is determined by a line bundle quotient of (O_Y)^{n+1}. In
this paper, we generalize this description to the case of maps from Y to an
arbitrary smooth toric variety. The data needed to determine such a map
consists of a collection of line bundles on Y together with a section of each
line bundle. Further... | 1993-12-03 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | David A. Cox (Amherst College) |
alg-geom/9312002 | Complete ideals defined by sign conditions and the real spectrum of a
two-dimensional local ring | This paper is about the local geometry of a real surfaces. It introduces
machinery for studying families of subsets which are determined by conditions
which are similar to base conditions, but also involve
positivity/non-negativity. The methods used are the real spectrum and Zariski's
theory of complete ideals. | 1993-12-03 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Dean Alvis, Bernard Johnston, James Madden |
alg-geom/9311013 | Remarks on Ein-Lazarsfeld criterion of spannedness of adjoint bundles of
polarized threefolds | Let B be a nef and big line bundle on a smooth complex threefold X with
canonical bundle K. Let x be a point on X and suppose that BC\ge3 for any curve
C passing x, B^2S\ge7 for any surface S containing x, and B^3\ge51. Then K+B is
spanned at x. (Ein-Lazarsfeld proved the assertion assuming B^3\ge92.)
Corollary: K+3L i... | 1993-11-30 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Takao Fujita (Tokyo Inst. of Tech.) |
alg-geom/9311011 | On the Brauer Group of Real Algebraic Surfaces | Let X be a real projective algebraic manifold, s numerates connected
components of X(R) and _2Br(X) the subgroup of elements of order 2 of the
cohomological Brauer group Br(X). We study the natural homomorphism \xi :
_2Br(X) \to (Z/2)^s and prove that \xi is epimorphic if H^3(X(C)/G;Z/2) \to
H^3(X(R);Z/2) is injective.... | 1993-11-28 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Viacheslav V. Nikulin |
alg-geom/9311010 | On Brauer Groups of Real Enriques Surfaces | Let Y be a real Enriques surface, _2Br(Y) the subgroup of elements of order 2
of Br(Y), and s, s_{or}, and s_{nor} the number of all connected, connected
orientable, and connected non-orientable components of Y(R) respectively. Using
universal covering K3-surface X of Y, we connect dim _2Br(Y) with the s, s_{or}
and s_... | 1993-11-28 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | V. V. Nikulin and R. Sujatha |
alg-geom/9311012 | On the Topological Classification of Real Enriques Surfaces. I | This note contains preliminary calculation of topological types or real
Enriques surfaces. We realize 59 topological types of real Enriques surfaces
(Theorem 6) and show that all other topological types belong to the list of 21
topological types (Theorem 7). In fact, our calculation contains much more
information which... | 1993-11-28 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Viacheslav V. Nikulin |
alg-geom/9311008 | Spin polynomial invariants for Dolgachev surfaces | We consider the spin polynomial invariants for bundles with c_2=2 and c_1 =
K_S + 2nk a rational mutiple of the canonical divisor on a Dolgacev surface. It
is shown that the chamber structure can be controlled so that the polynomials
give diffeomorphism invariants of Dolgachev surfaces of the form q_S(n) =
a(n)Q^2 + b(... | 1993-11-23 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | S. Bauer and V. Pidstrigatch |
alg-geom/9311007 | On the Picard Number of Fano 3-Folds with Terminal Singularities | We prove the following main result: Let X be a Fano 3-fold with terminal
Q-factorial singularities and X does not have a small extremal ray and a face
of Kodaira dimension 1 or 2 for Mori polyhedron of X. Then the Picard number
\rho (X) < 8. | 1993-11-19 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Viacheslav V. Nikulin |
alg-geom/9311006 | Surfaces of Degree 10 in the Projective Fourspace via Linear Systems and
Linkage | The paper discusses the classification of surfaces of degree 10 and sectional
genus 9 and 10. The surfaces of degree at most 9 are described through
classical work dating from the last century up to recent years, while surfaces
of degree 10 and other sectional genera are studied elsewhere.
We use relations between mu... | 1993-11-16 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Sorin Popescu and Kristian Ranestad |
alg-geom/9311005 | Irreducibility of Moduli Spaces of Vector Bundles on Birationally Ruled
Surfaces | Let $S$ be a birationally ruled surface. We show that the moduli schemes
$M_S(r,c_1,c_2)$ of semistable sheaves on $S$ of rank $r$ and Chern classes
$c_1$ and $c_2$ are irreducible for all $(r,c_1,c_2)$ provided the polarization
of $S$ used satisfies a simple numerical condition. This is accomplished by
proving that th... | 1993-11-16 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Charles Walter |
alg-geom/9311004 | On discrete Zariski-dense subgroups of algebraic groups | We investigate for which linear-algebraic groups (over the complex numbers or
any local field) there exists subgroups which are dense in the Zariski
topology, but discrete in the Hausdorff topology. For instance, such subgroups
exist for every non-solvable complex group. | 1993-11-14 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | J. Winkelmann |
alg-geom/9311003 | Geometric height inequality on varieties with ample cotangent bundles | Let F be a function field of one variable over an algebraically closed field
of characteristic zero, X a geometrically irreducible smooth projective variety
over F, and L a line bundle on X. In this note, we will prove that if the
contangent bundle of X is ample and X is non-isotrivial, then there are a
proper closed a... | 1993-11-10 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Atsushi Moriwaki |
alg-geom/9311002 | Projective Degenerations of K3 Surfaces, Gaussian Maps, and Fano
Threefolds | In this article we exhibit certain projective degenerations of smooth $K3$
surfaces of degree $2g-2$ in $\Bbb P^g$ (whose Picard group is generated by the
hyperplane class), to a union of two rational normal scrolls, and also to a
union of planes. As a consequence we prove that the general hyperplane section
of such $K... | 1993-11-09 | 2009-10-22 | [
"alg-geom",
"math.AG"
] | Ciro Ciliberto, Angelo Lopez, and Rick Miranda |
alg-geom/9311001 | On Banica sheaves and Fano manifolds | In the present paper we discuss coherent sheaves of rank > 1 whose
projectivization gives rise to smooth varieties - varieties of this type are
also called smooth scrolls. We prove some basic properties of these varieties
and we give some pertinent examples. We classify Fano manifolds of large index
which are of this t... | 1993-11-07 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Edoardo Ballico and Jaroslaw Wisniewski |
alg-geom/9310008 | A Propos de l'Existence de Fibr\'es Stables sur les Surfaces | We prove the existence (in characteristic 0) on every polarized (smooth,
projective and connected) surface of stable bundles of rank $r\geq 2$,
arbitrary first Chern class and large enough $c_2$. | 1993-10-29 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Andr\'e Hirschowitz, Yves Laszlo |
alg-geom/9310007 | Initial ideals, Veronese subrings, and rates of algebras | We show that high Veronese subrings of any commutative graded ring have a
Grobner basis with all relations of degree 2. (The d-th Veronese subring of a
ring A_0 + A_1 + A_2 + ... is the ring A_0 + A_d + A_{2d} + ...; ``high'' means
we take d sufficiently large, say at least half the regularity of the ideal
defining the... | 1993-10-11 | 2008-02-03 | [
"alg-geom",
"math.AC",
"math.AG"
] | David Eisenbud, Alyson Reeves, and Burt Totaro |
alg-geom/9310005 | Teichm\"uller Theory and the Universal Period Mapping via Quantum
Calculus and the $H^{1/2}$ Space on the Circle | The Universal Teichm\"uller Space, $T(1)$, is a universal parameter space for
all Riemann surfaces. In earlier work of the first author it was shown that one
can canonically associate infinite- dimensional period matrices to the
coadjoint orbit manifold $Diff(S^1)/Mobius(S^1)$ -- which resides within $T(1)$
as the (Kir... | 1993-10-07 | 2008-02-03 | [
"alg-geom",
"funct-an",
"hep-th",
"math.AG",
"math.FA"
] | Subhashis Nag and Dennis Sullivan |
alg-geom/9310006 | Torsion Sections of Elliptic Surfaces | Given a torsion section of a semistable elliptic surface, we prove
equidistribution results for the components of singular fibers which are hit by
the section, and for the root of unity (identifying the zero component with
${\Bbb C}$) which is hit by the section in case the section hits the zero
component. | 1993-10-07 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Rick Miranda and Peter F. Stiller |
alg-geom/9310002 | General hyperplane sections of nonsingular flops in dimension 3 | We give a simple proof of a theorem of Katz and Morrison. | 1993-10-05 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Yujiro Kawamata |
alg-geom/9310004 | Quantum Cohomology Rings of Toric Manifolds | We compute the quantum cohomology ring $H^*_{\varphi}({\bf P}, {\bf C})$ of
an arbitrary $d$-dimensional smooth projective toric manifold ${\bf
P}_{\Sigma}$ associated with a fan $\Sigma$. The multiplicative structure of
$H^*_{\varphi}({\bf P}_{\Sigma}, {\bf C})$ depends on the choice of an element
$avarphi$ in the ord... | 1993-10-05 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Victor V. Batyrev |
alg-geom/9310003 | Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric
Varieties | We consider families ${\cal F}(\Delta)$ consisting of complex
$(n-1)$-dimensional projective algebraic compactifications of $\Delta$-regular
affine hypersurfaces $Z_f$ defined by Laurent polynomials $f$ with a fixed
$n$-dimensional Newton polyhedron $\Delta$ in $n$-dimensional algebraic torus
${\bf T} =({\bf C}^*)^n$. ... | 1993-10-05 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Victor V. Batyrev |
alg-geom/9310001 | Towards the Mirror Symmetry for Calabi-Yau Complete intersections in
Gorenstein Toric Fano Varieties | We propose a combinatorical duality for lattice polyhedra which conjecturally
gives rise to the pairs of mirror symmetric families of Calabi-Yau complete
intersections in toric Fano varieties with Gorenstein singularities. Our
construction is a generalization of the polar duality proposed by Batyrev for
the case of hyp... | 1993-10-02 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Lev Borisov |
alg-geom/9309007 | The Monomial-Divisor Mirror Map | For each family of Calabi-Yau hypersurfaces in toric varieties, Batyrev has
proposed a possible mirror partner (which is also a family of Calabi-Yau
hypersurfaces). We explain a natural construction of the isomorphism between
certain Hodge groups of these hypersurfaces, as predicted by mirror symmetry,
which we call th... | 1993-09-30 | 2008-02-03 | [
"alg-geom",
"hep-th",
"math.AG"
] | Paul S. Aspinwall, Brian R. Greene and David R. Morrison |
alg-geom/9309006 | Conic bundles in projective fourspace | P. Ellia and G.Sacchiero have shown that if $S$ is a smooth surface in $\Pn
4$ which is ruled in conics, then $S$ has degree 4 or 5. In this paper we give
a proof of this result combining the ideas of Ellia and Sacchiero as they are
used in the paper of the second author on plane curve fibrations and the recent
work of... | 1993-09-27 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Robert Braun and Kristian Ranestad |
alg-geom/9309005 | Differential-geometric methods for the lifting problem and linear
systems on plane curves | Let $X$ be an integral projective variety of codimension two, degree $d$ and
dimension $r$ and $Y$ be its general hyperplane section. The problem of lifting
generators of minimal degree $\sigma$ from the homogeneous ideal of $Y$ to the
homogeneous ideal of $X$ is studied. A conjecture is given in terms of $d$, $r$
and ... | 1993-09-23 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Emilia Mezzetti |
alg-geom/9309004 | Generic Singularities of Holomorphic Foliations | A holomorphic foliation is defined as an integrable coherent subsheaf of the
tangent sheaf. The structure of the leaves around a singularity is read off
from the structure of the stalks. This was done by Baum when the dimension of
the singular set is one less than the leaf dimension. In this article we study
the genera... | 1993-09-21 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Sinan Sertoz |
alg-geom/9309003 | Conformal blocks and generalized theta functions | Let M(r) be the moduli space of rank r vector bundles with trivial
determinant on a Riemann surface X . This space carries a natural line bundle,
the determinant line bundle L . We describe a canonical isomorphism of the
space of global sections of L^k with a space known in conformal field theory as
the ``space of conf... | 1993-09-15 | 2009-10-22 | [
"alg-geom",
"math.AG"
] | Arnaud Beauville and Yves Laszlo |
alg-geom/9309002 | A family of \'etale coverings of the affine line | In the note we construct a family of \'etale coverings of the affine line.
More specifically, let $F$ be a finite field of characteristic $p$ and suppose
that the cardinality of $F$ is at least 4. Let $A = F[T]$ be the polynomial
ring in one variable $T$, $K=F(T)$. Let $K_\infty$ be the completion of $K$
along the valu... | 1993-09-02 | 2015-06-30 | [
"alg-geom",
"math.AG"
] | Kirti Joshi (School of Mathematics, Tata Institute of Fundamental
Research, Bombay) |
alg-geom/9309001 | Theoremes de connexites et varietes abeliennes | We prove a connexity theorem for abelian varieties in characteristic $0$: if
$X$ is an abelian variety and $V\rightarrow X$ and $W\rightarrow X$ two
morphisms, then, under certain hypotheses, the fiber product of $V$ and $W$
over $X$ is connected. This theorem has several consequences: the algebraic
fundamental groups ... | 1993-09-01 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Olivier Debarre |
alg-geom/9308006 | Unobstructedness of Calabi-Yau OrbiKleinfolds | We show that Calabi-Yau spaces with certain types of hypersurface- quotient
singularities have unobstructed deformations. This applies in particular to all
Calabi-Yau orbifolds nonsingular in codimension 2. | 1993-08-31 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Z. Ran |
alg-geom/9308005 | The existence of higher logarithms | In this paper we prove the existence of all higher logarithms as multivalued
and ordinary Deligne cohomology classes. | 1993-08-31 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Richard Hain |
alg-geom/9308004 | Vector bundles and $SO(3)$ invariants for elliptic surfaces III: The
case of odd fiber degree | This paper, the last in a series of three, studies vector bundles on an
elliptic surface whose determinant has odd intersection number with a general
fiber and uses this study to calculate certain coefficients of Donaldson
polynomials. | 1993-08-23 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Robert Friedman |
alg-geom/9308003 | Some remarks on the Kronheimer-Mrowka classes of algebraic surfaces | Define the Donaldson series of a simply connected 4-manifold by
q(X) = \sum_d q_d(X)/d!
Recently Kronheimer and Mroka have announced the result that the Donaldson
series of so called simple 4-manifolds can be written as
q(X) = e^{Q/2}\sum_{i=1}^p a_i e^{K_i}
where $Q$ is the intersection form and the $K_i \in H... | 1993-08-20 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | R. Brussee |
alg-geom/9308002 | The Euler Series of Restricted Chow Varieties | Let X be an algebraic projective variety in {\bf P}^n. Denote by {\cal
C}_{\lambda} the space of all effective cycles on X whose homology class is
\lambda \in H_{2p} (X,{\bf Z}). It is easy to show that {\cal C}_{\lambda} is
an algebraic projective variety. Let \chi ({\cal C}_{\lambda} be its Euler
characteristic. Defi... | 1993-08-11 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Javier Elizondo |
alg-geom/9308001 | On the Griffiths group of the cubic sevenfold | We prove that the Griffiths group of 3-cycles homologous to zero modulo
algebraic equivalence, on a generic hypersurfaces of dimension 7 and degree 3
is not finitely generated, even when tensored with Q. Using this and a result
of Nori, we give examples of varieties for which some Griffiths group is not
finitely genera... | 1993-08-03 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Alberto Albano and Alberto Collino |
alg-geom/9307010 | Generalized Hypergeometric Functions and Rational Curves on Calabi-Yau
Complete Intersections in Toric Varieties | We formulate general conjectures about the relationship between the A-model
connection on the cohomology of a $d$-dimensional Calabi-Yau complete
intersection $V$ of $r$ hypersurfaces $V_1, \ldots, V_r$ in a toric variety
${\bf P}_{\Sigma}$ and the system of differential operators annihilating the
special hypergeometri... | 1993-07-30 | 2009-10-22 | [
"alg-geom",
"math.AG"
] | Victor V. Batyrev and Duco van Straten |
alg-geom/9307009 | Hyperkaehler and holomorphic symplectic geometry | We prove that all complex analytic subvarieties of a generic compact
hyperkaehler manifold are even-dimensional. Moreover, these subvarieties are
holomorphically symplectic. | 1993-07-29 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Misha Verbitsky |
alg-geom/9307008 | Hyperholomorphic bundles | Hyperholomorphic bundle is a bundle with connection defined over a
hyperkaehler manifold such that this connection is holomorphic with respect to
all complex structures induced by a hyperkaehler structure. A hyperholomorphic
connection is Yang-Mills. If a stable bundle has first two Chern classes
invariant with respect... | 1993-07-29 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Misha Verbitsky |
alg-geom/9307006 | Boundary of the Picard Group of a Singular Curve | In this work we explore the boundary of the jacobian of a singular curve in
the compactified picard group. We formulate a functor that helps to determine
this boundary and show that this functor is representable. We try to dertermine
the points on the boundary. | 1993-07-24 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Jyotsna Gokhale |
alg-geom/9307007 | Compactified Jacobian of some Singular Curves | We look at the decomposition of the compactified jacobian of a singular curve
into components and discuss some examples. | 1993-07-24 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Jyotsna Gokhale |
alg-geom/9307005 | Duistermaat-Heckman measures in a non-compact setting | We prove a \dh type formula in a suitable non-compact setting. We use this
formula to evaluate explicitly the pushforward of the Liouville measure via the
moment map of both an abelian and a non-abelian group action. As an application
we obtain the classical analogues of well-known multiplicity formulas for the
holomor... | 1993-07-21 | 2008-02-03 | [
"alg-geom",
"hep-th",
"math.AG"
] | Elisa Prato and Siye Wu |
alg-geom/9307004 | Arithmetic Bogomolov-Gieseker's inequality | Let f : X --> Spec(Z) be an arithmetic variety of dimension d >= 2 and (H, k)
an arithmetically ample Hermitian line bundle on X. Let (E, h) be a rank r
vector bundle on X. In this paper, we will prove that if E is semistable with
respect to H on each connected component of the infinite fiber of X, then
{ c_2(E, h) -... | 1993-07-19 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Atsushi Moriwaki |
alg-geom/9307002 | Vector bundles and $SO(3)$ invariants for elliptic surfaces I | This paper is the first in a series of three devoted to the smooth
classification of simply connected elliptic surfaces. The method is to compute
some coefficients of Donaldson polynomials of $SO(3)$ invariants whose second
Stiefel-Whitney class is transverse to the unique primitive class $\kappa$ such
that a positive ... | 1993-07-14 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Robert Friedman |
alg-geom/9307003 | Vector bundles and $SO(3)$ invariants for elliptic surfaces II: The case
of even fiber degree | This paper is the second in a series of three devoted to the smooth
classification of simply connected elliptic surfaces. In this paper, we study
the case where one of the multiple fibers has even multiplicity, and describe
the moduli space of stable rank two vector bundles with the appropriate first
Chern class needed... | 1993-07-14 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Robert Friedman |
alg-geom/9307001 | Localization for nonabelian group actions | Suppose $X$ is a compact symplectic manifold acted on by a compact Lie group
$K$ (which may be nonabelian) in a Hamiltonian fashion, with moment map $\mu: X
\to {\rm Lie}(K)^*$ and Marsden-Weinstein reduction $\xred = \mu^{-1}(0)/K$.
There is then a natural surjective map $\kappa_0$ from the equivariant
cohomology $H^*... | 1993-07-06 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | L.C. Jeffrey and F.C. Kirwan |
alg-geom/9306011 | On the Hodge Structure of Projective Hypersurfaces in Toric Varieties | This paper generalizes classical results of Griffiths, Dolgachev and
Steenbrink on the cohomology of hypersurfaces in weighted projective spaces.
Given a $d$-dimensional projective simplicial toric variety $P$ and an ample
hypersurface $X$ defined by an polynomial $f$ in the homogeneous coordinate
ring $S$ of $P$ (as d... | 1993-06-25 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Victor V. Batyrev (Essen) and David A. Cox (Amherst College) |
alg-geom/9306009 | Classification of smooth congruences with a fundamental curve | We give a classification and a construction of all smooth $(n-1)$-dimensional
varieties of lines in ${\bf P}\sp n$ verifying that all their lines meet a
curve. This also gives a complete classification of $(n-1)$-scrolls over a
curve contained in $G(1,n)$. | 1993-06-23 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Enrique Arrondo, Marina Bertolini and Cristina Turrini |
alg-geom/9306010 | On stability of tangent bundles of Fano manifolds with b_2=1 | In the present paper we discuss stability of the tanget bundle of a Fano
n-fold of index >= n-2 and b_2=1. For example, we prove that all Fano 4-folds
with b_2=1 have stable tangent bundle. For this purpose we prove some vanishing
theorems for sheaves of twisted holomorphic forms on ample divisors and cyclic
coverings ... | 1993-06-22 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Thomas Peternell, Jaroslaw A. Wisniewski |
alg-geom/9306008 | Distribution of Energy Levels of a Quantum Free Particle on a Surface of
Revolution | We prove that the error term $\La(R)$ in the Weyl asymptotic formula $$\#\{
E_n\le R^2\}={\Vol M\over 4\pi} R^2+\La(R),$$ for the Laplace operator on a
surface of revolution $M$ satisfying a twist hypothesis, has the form $\La(R)
=R^{1/2}F(R)$ where $F(R)$ is an almost periodic function of the Besicovitch
class $B^2$, ... | 1993-06-18 | 2008-02-03 | [
"alg-geom",
"hep-th",
"math.AG"
] | Pavel Bleher |
alg-geom/9306007 | Trisecant Lines And Jacobians, II | Let $\Theta$ be a symmetric theta divisor on an indecomposable principally
polarized complex abelian variety $X$. The linear system $|2\Theta |$ defines a
morphism $K:X\ra |2\Theta |^*$, whose image is the Kummer variety $K(X)$ of
$X$. When $(X,\theta)$ is the Jacobian of an algebraic curve, there are
infinitely many t... | 1993-06-18 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Olivier Debarre |
alg-geom/9306006 | Bogomolov Instability and Kawamata-Viehweg Vanishing | The purpose of this note is to show how the Kawamata-Viehweg vanishing
theorem for fractional divisors leads to a quick new proof of Bogomolov's
instability theorem for rank two vector bundles on an algebraic surface. | 1993-06-17 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Guillermo Fernandez del Busto |
alg-geom/9306005 | Gromov Invariants for Holomorphic Maps from Riemann Surfaces to
Grassmannians | Two compactifications of the space of holomorphic maps of fixed degree from a
compact Riemann surface to a Grassmannian are studied. It is shown that the
Uhlenbeck compactification has the structure of a projective scheme and is
dominated by the algebraic compactification arising as a Grothendieck Quot
scheme. The latt... | 1993-06-08 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Aaron Bertram, Georgios Daskalopoulos, Richard Wentworth |
alg-geom/9306004 | Very ample linear systems on abelian varieties | Let $(X,L)$ be a polarized complex abelian variety of dimension $g$ where $L$
is a polarization of type $(1,...,1,d)$. For $(X,L)$ genberic we prove the
following:
(1) If $d \ge g+2$, then $\phi_L\colon X \to {\bf P}^{d-1}$ defines a
birational morphism onto its image.
(2) If $d > 2^g$, then $L$ is very ample.
We... | 1993-06-04 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | O. Debarre, K. Hulek, J. Spandaw |
alg-geom/9306003 | Linear Structure on Calabi-Yau Moduli Spaces | We show that the formal moduli space of a Calabi-Yau manifold $X^n$ carries a
linear structure, as predicted by mirror symmetry. This linear structure is
canonically associated to a splitting of the Hodge filtration on $H^n(X)$. | 1993-06-03 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Z. Ran |
alg-geom/9306001 | The automorphism group of the moduli space of semi stable vector bundles | Let ${\cal S}{\cal U}(r, L_0)$ denote the moduli space of semi stable vector
bundles of rank $r$ and fixed determinant $L_0$ of degree $d$ on a smooth curve
$C$ of genus $g \geq 3$. In this paper we describe the group of automorphisms
of $ {\cal S}{\cal U}(r, L_0) $. The analogue of this result is carried out for
the s... | 1993-06-02 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Alexis Kouvidakis and Tony Pantev |
alg-geom/9306002 | Picard groups of Hilbert schemes of curves | We calculate the Picard group, over the integers, of the Hilbert scheme of
smooth, irreducible, non-degenerate curves of degree $d$and genus $g \geq 4$ in
${\Bbb P}^r$, in the case when $d \geq 2g+1 $ and $r \leq d-g$. We express the
classes of the generators in terms of some ``natural'' divisor classes. | 1993-06-02 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Alexis Kouvidakis |
alg-geom/9305012 | A Kaehler Structure on the Space of String World-Sheets | Let (M,g) be an oriented Lorentzian 4-manifold, and consider the space S of
oriented, unparameterized time-like 2-surfaces in M (string world-sheets) with
fixed boundary conditions. Then the infinite-dimensional manifold S carries a
natural complex structure and a compatible (positive-definite) Kaehler metric h
on S de... | 1993-05-26 | 2009-10-22 | [
"alg-geom",
"math.AG"
] | Claude LeBrun |
alg-geom/9305010 | Finding Sparse Systems of Parameters | For several computational procedures such as finding radicals and Noether
normalizations, it is important to choose as sparse as possible a system of
parameters in a polynomial ideal or modulo a polynomial ideal. We describe new
strategies for these tasks, thus providing solutions to problems (1) and (2)
posed in [Eise... | 1993-05-20 | 2008-02-03 | [
"alg-geom",
"math.AC",
"math.AG"
] | David Eisenbud and Bernd Sturmfels |
alg-geom/9305011 | On the fundamental group of an abelian cover | We study the behaviour of the topological fundamental group under totally
ramified abelian covers (a special case of abelian Galois covers) of complex
projective varieties of dimension at least 2. | 1993-05-20 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Rita Pardini, Francesca Tovena |
alg-geom/9305007 | An inequality for polynomial mappings | We give an estimate of the growth of a polynonial mapping of $C^n$. | 1993-05-19 | 2016-08-14 | [
"alg-geom",
"math.AG"
] | Arkadiusz P{\l}oski |
alg-geom/9305008 | Injectivity on one line | Let $k$ be an algebraically closed field of characteristic zero. Let
$H:k^2\to k^2$ be a polynomial mapping such that the Jacobian $\text{Jac}\,H$
is a non-zero constant. In this note we prove, that if there is a line $l
\subset k^2$ such that $H|_l:l\to k^2$ is an injection, then $H$ is a
polynomial automorphism. | 1993-05-19 | 2016-08-14 | [
"alg-geom",
"math.AG"
] | Janusz Gwo\'zdziewicz |
alg-geom/9305006 | The Noether exponent and Jacobi formula | For any polynomial mapping $F=(F_1,\dots ,F_n)$ of $\Cal C^n$ with a finite
number of zeros we define the Noether exponent $\nu(F)$. We prove the Jacobi
formula for all polynomials of degree strictly less than $\sum_{i=1}^n (\deg
F_i-1)-\nu(F)$. | 1993-05-19 | 2016-08-14 | [
"alg-geom",
"math.AG"
] | Arkadiusz P{\l}oski |
alg-geom/9305009 | On the approximate roots of polynomials | We give a simplified approach to the Abhyankar--Moh theory of approximate
roots. Our considerations are based on properties of the intersection
multiplicity of local curves. | 1993-05-19 | 2016-08-14 | [
"alg-geom",
"math.AG"
] | Janusz Gwo\'zdziewicz and Arkadiusz P{\l}oski |
alg-geom/9305005 | Inequality of Bogomolov-Gieseker's type on arithmetic surfaces | Let K be an algebraic number field, O_K the ring of integers of K, and f : X
--> Spec(O_K) an arithmetic surface. Let (E, h) be a rank r Hermitian vector
bundle on X such that $E$ is semistable on the geometric generic fiber of f. In
this paper, we will prove an arithmetic analogy of Bogomolov-Gieseker's
inequality: c_... | 1993-05-12 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Atsushi Moriwaki |
alg-geom/9305004 | Kodaira energies of polarized log varieties | Let L be an ample line bundle on a log variety (V, D) having only log
terminal singularities.The Kodaira energy of such a triple (V, D, L) is defined
as follows: \kappa\epsilon=-Inf{t\in Q | K(V,D)+tL is big}. Here K(V,D)=K_V+D
is the log canonical bundle of (V,D) and "big" means \kappa=dim V. We first
show that the ra... | 1993-05-07 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | T. Fujita |
alg-geom/9305003 | Log contractions and equidimensional models of elliptic threefolds | This work was initially motivated by Miranda's work on elliptic Weierstrass
threefolds. Miranda [Mi] describes a smooth equidimensional (flat) model for
any elliptic Weierstrass threefold; such models occur naturally in the study of
moduli spaces. In this paper we use minimal model theory to link birational
maps of log... | 1993-05-05 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | A. Grassi |
alg-geom/9305002 | A Finiteness Theorem for Elliptic Calabi-Yau Threefolds | We prove that up to birational equivalence, there exists only a finite number
of families of Calabi-Yau threefolds (i.e. a threefold with trivial canonical
class and factorial terminal singularities) which have an elliptic fibration to
a rational surface. This strengthens a result of B. Hunt that there are only a
finit... | 1993-05-03 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | M. Gross |
alg-geom/9305001 | A General Noether-Lefschetz Theorem and applications | In this paper we generalize the classical Noether-Lefschetz Theorem to
arbitrary smooth projective threefolds. Let $X$ be a smooth projective
threefold over complex numbers, $L$ a very ample line bundle on $X$. Then we
prove that there is a positive integer $n_0(X,L)$ such that for $n \geq
n_0(X,L)$, the Noether-Lefsch... | 1993-05-03 | 2024-07-09 | [
"alg-geom",
"math.AG"
] | Kirti Joshi |
alg-geom/9304007 | Compactifications of moduli spaces inspired by mirror symmetry | We study moduli spaces of nonlinear sigma-models on Calabi-Yau manifolds,
using the one-loop semiclassical approximation. The data being parameterized
includes a choice of complex structure on the manifold, as well as some ``extra
structure'' described by means of classes in H^2. The expectation that this
moduli space ... | 1993-04-23 | 2008-02-03 | [
"alg-geom",
"hep-th",
"math.AG"
] | David R. Morrison |
alg-geom/9304006 | Recovering of curves with involution by extended Prym data | With every smooth, projective algebraic curve $\tilde{C}$ with involution
$\sigma :\tilde{C}\longrightarrow \tilde{C}$ without fixed points is associated
the Prym data which consists of the Prym variety $P:=(1-\sigma )J(\tilde{C})$
with principal polarization $\Xi$ such that $2\Xi$ is algebraically equivalent
to the re... | 1993-04-14 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Vassil Kanev |
alg-geom/9304005 | Schur quadrics, cubic surfaces and rank 2 vector bundles over the
projective plane | A cubic surface in $P^3$ is known to contain 27 lines, out of which one can
form 36 Schlafli double - sixes i.e., collections $l_1,...,l_6, l'_1,...,
l'_6\}$ of 12 lines such that each $l_i$ meets only $l'_j, j\neq i$ and does
not meet $l_j, j\neq i$. In 1881 F. Schur proved that any double - six gives
rise to a certai... | 1993-04-13 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | I. Dolgachev and M. Kapranov |
alg-geom/9304004 | Holomorphic Slices, Symplectic Reduction and Multiplicities of
Representations | I prove the existence of slices for an action of a reductive complex Lie
group on a K\"ahler manifold at certain orbits, namely those orbits that
intersect the zero level set of a momentum map for the action of a compact real
form of the group. I give applications of this result to symplectic reduction
and geometric qu... | 1993-04-12 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Reyer Sjamaar |
alg-geom/9304003 | What can be computed in algebraic geometry? | This paper is a survey of computational issues in algebraic geometry, with
particular attention to the theory of Grobner bases and the regularity of an
algebraic variety.
1. A geometric introduction to Grobner bases.
2. An algebraic introduction to Grobner bases.
3. Bounds in algebraic geometry, and regularity an... | 1993-04-11 | 2015-06-30 | [
"alg-geom",
"math.AG"
] | Dave Bayer and David Mumford |
alg-geom/9304002 | Refined intersection products and limiting linear subspaces of
hypersurfaces | Let $X$ be a hypersurface of degree $d$ in $\Bbb P^n$ and $F_X$ be the scheme
of $\Bbb P^r$'s contained in $X$. If $X$ is generic, then $F_X$ will have the
expected dimension (or empty) and its class in the Chow ring of $G(r+1,n+1)$ is
given by the top Chern class of the vector bundle $S^dU^*$, where $U$ is the
univers... | 1993-04-07 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Xian Wu |
alg-geom/9304001 | Birational Equivalences of Vortex Moduli | We construct a finite dimensional Kaehler manifold with a holomorphic,
symplectic circle action whose symplectic reduced spaces may be identified with
the tau-vortex moduli spaces (or tau-stable pairs). The Morse theory of the
circle action induces natural birational maps between the reduced spaces for
different values... | 1993-04-06 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | S. Bradlow, G. Daskalopoulos, and R. Wentworth |
alg-geom/9303007 | The Variety of Positive Superdivisors of a Supercurve (Supervortices) | The supersymmetric product of a supercurve is constructed with the aid of a
theorem of algebraic invariants and the notion of positive relative
superdivisor (supervortex) is introduced. A supercurve of positive
superdivisors of degree 1 (supervortices of vortex number 1) of the original
supercurve is constructed as its... | 1993-03-29 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | J.A. Dominguez Perez, D. Hernandez Ruiperez and C. Sancho de Salas |
alg-geom/9303005 | Free pencils on divisors | Let X be a smooth projective variety defined over an algebraically closed
field, and let Y in X be a reduced and irreducible ample divisor in X. We give
a numerical sufficient condition for a base point free pencil on $Y$ to be the
restriction of a base point free pencil on $X$. This result is then extended to
families... | 1993-03-28 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Roberto Paoletti |
alg-geom/9303006 | Seshadri constants, gonality of space curves and restriction of stable
bundles | We define the Seshadri constant of a space curve and consider ways to
estimate it. We then show that it governs the gonality of the curve. We use an
argument based on Bogomolov's instability theorem on a threefold. The same
methods are then applied to the study of the behaviour of a stable vector
bundle on P^3 under re... | 1993-03-28 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Roberto Paoletti |
alg-geom/9303004 | Theta Functions for $\SL(n)$ versus $\GL(n)$ | Over a smooth complex projective curve $C$ of genus $g$ let $\M (n,d)$ be the
moduli space of semistable bundles of rank $n$ and degree $d$ on $C$, and $\SM
(n,L)$, the moduli space of those bundles whose determinant is isomorphic to a
fixed line bundle $L$ over $C$. Let $\theta_F$ and $\theta$ be theta bundles
over th... | 1993-03-28 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Ron Donagi and Loring W. Tu |
alg-geom/9303003 | Deformations of cones over hyperelliptic curves | We determine the versal deformation of cones, in the simplest case: cones
over hyperelliptic curves of high degree. In particular, we show that for
degree $4g+4$, the highest degree for which interesting deformations exist, the
number of smoothing components is $2^{2g+1}$ ($g\neq3$).
We review in a general setting th... | 1993-03-23 | 2015-06-30 | [
"alg-geom",
"math.AG"
] | Jan Stevens |
alg-geom/9303002 | Projective varieties with many degenerate subvarieties | We study the problem of classifying the irreducible projective varieties $X$
of dimension $n\ge 2$ in $\Bbb P^N$ which contain an algebraic family $\Cal F$
of dimension $h+1$ ($h<n$) of subvarieties $Y$ of dimension $n-h$, each one
contained in a $\Bbb P^{N-h-1}$. We prove that one of the following happens:
(i) there e... | 1993-03-20 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Emilia Mezzetti |
alg-geom/9303001 | Semistable Minimal Models of Threefolds in Positive or Mixed
Characteristic | We extend the minimal model theorem to the 3-dimensional schemes which are
projective and have semistable reduction over the spectrum of a Dedekind ring. | 1993-03-05 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Yujiro Kawamata |
alg-geom/9302006 | Existence and Deformation Theory for Scalar-Flat Kaehler Metrics on
Compact Complex Surfaces | Let M be a compact complex surface which admits a Kaehler metric whose scalar
curvature has integral zero; and suppose the fundamental group of M does not
contain an Abelian subgroup of finite index. Then if M is blown up at
sufficiently many points, the resulting surface M' admits scalar-flat Kaehler
metrics. | 1993-02-23 | 2009-10-22 | [
"alg-geom",
"math.AG"
] | Claude LeBrun and Michael Singer |
alg-geom/9302005 | A Finiteness Theorem for Quaternionic-Kaehler Manifolds with Positive
Scalar Curvature | We study the topology and geometry of those compact Riemannian (4n)-manifolds
(M,g), n > 1, with positive scalar curvature and holonomy in Sp(n)Sp(1). Up to
homothety, we show that there are only finitely many such manifolds of any
dimension 4n. | 1993-02-23 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Claude LeBrun |
alg-geom/9302004 | Intersection homology Betti numbers | A generalization of the formula of Fine and Rao for the ranks of the
intersection homology groups of a complex algebraic variety is given. The proof
uses geometric properties of intersection homology and mixed Hodge theory. | 1993-02-12 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Alan H. Durfee |
alg-geom/9302003 | Lefschetz Fixed Point Theorem and Lattice Points in Convex Polytopes | A simple convex lattice polytope $\Box$ defines a torus-equivariant line
bundle $\LB$ over a toric variety $\XB.$ Atiyah and Bott's Lefschetz
fixed-point theorem is applied to the torus action on the $d''$-complex of
$\LB$ and information is obtained about the lattice points of $\Box$. In
particular an explicit formula... | 1993-02-09 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Sacha Sardo-Infirri |
alg-geom/9302002 | On the surjectivity of Wahl maps on a general curve | This paper explores the geometric meaning of the failure of certain kinds of
Wahl maps to surject on a general curve. Sufficient conditions for surjectivity
are given. An approach used by Voisin to study canonical Wahl maps is applied
in this direction. | 1993-02-09 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Roberto Paoletti |
alg-geom/9302001 | A note on non-vanishing and applications | Let $X$ be a normal variety over the field of complex numbers with log
terminal singularities and the canonical divisor $K_X$ being ${\bf
Q}$-Gorenstein. Assume that $L$ is an ample line bundle over $X$ and $\phi:
X\to Y$ is a morphism supported by $K_X+rL$ for some positive rational number
$r$. In the present paper we... | 1993-02-01 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Marco Andreatta, Jaros{\l}aw A. Wi\'sniewski |
alg-geom/9301007 | Bounds of automorphism groups of genus 2 fibrations | For a complex surface of general type with a relatively minimal genus 2
fibration, the bounds of the orders of the automorphism group of the fibration,
of its abelian subgroups and of its cyclic subgroups are determined as linear
functions of $c^2_1$. Most of them are the best. | 1993-01-29 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Zhi-Jie Chen |
alg-geom/9301006 | Rational curves on Calabi-Yau manifolds: verifying predictions of Mirror
Symmetry | Mirror symmetry, a phenomenon in superstring theory, has recently been used
to give tentative calculations of several numbers in algebraic geometry. In
this paper, the numbers of lines and conics on various hypersurfaces which
satisfy certain incidence properties are calculated, and shown to agree with
the numbers pred... | 1993-01-27 | 2008-02-03 | [
"alg-geom",
"hep-th",
"math.AG"
] | Sheldon Katz |
alg-geom/9301005 | The topology of the space of rational curves on a toric variety | Let $X$ be a compact toric variety. Let $Hol$ denote the space of based
holomorphic maps from $CP^1$ to $X$ which lie in a fixed homotopy class. Let
$Map$ denote the corresponding space of continuous maps. We show that $Hol$ has
the same homotopy groups as $Map$ up to some (computable) dimension. The proof
uses a descr... | 1993-01-24 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Martin A. Guest |
alg-geom/9301004 | The Geometry of Bielliptic Surfaces in P^4 | In 1988 Serrano \cite{Ser}, using Reider's method, discovered a minimal
bielliptic surface in $\PP^4$. Actually he showed that there is a unique family
of such surfaces and that they have degree 10 and sectional genus 6. In this
paper we describe, among other things, the geometry of the embedding of the
minimal biellip... | 1993-01-20 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | A. Aure, W. Decker, K. Hulek, S. Popescu, K. Ranestad |
alg-geom/9301002 | Minimal Cohomology Classes and Jacobians | We show that on the Jacobian $(JC,\theta)$ of a smooth curve $C$ of genus
$g$, any effective cycle in $JC$ with cohomology class $\theta^d/d!$ is a
translate of $W_{g-d}(C)$ or $-W_{g-d}(C)$. We then use this result to prove
that for $1<d<g$, the Jacobian locus (\resp the locus of intermediate Jacobians
of cubic threef... | 1993-01-06 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Olivier Debarre |
alg-geom/9301003 | Non-trivial Linear Systems on Smooth Plane Curves | Let $C$ be a smooth plane curve of degree $d$ defined over an algebraically
closed field $k$. A base point free complete very special linear system $g^r_n$
on $C$ is trivial if there exists an integer $m\ge 0$ and an effective divisor
$E$ on $C$ of degree $md-n$ such that $g^r_n=|mg^2_d-E|$ and
$r=(m^2+3m)/2-(md-n)$. I... | 1993-01-06 | 2008-02-03 | [
"alg-geom",
"math.AG"
] | Marc Coppens and Takao Kato |
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